Details

Time bar (total: 2.1m)

sample248.0ms

Algorithm
intervals
Results
63.0ms52×body1280valid
28.0ms36×body640valid
23.0ms144×body80valid
8.0ms13×body320valid
3.0ms11×body160valid

simplify148.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
147.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.2b
(- 1 (* (tan x) (tan x)))
0.2b
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
24×add-cube-cbrt
18×pow1
15×times-frac
10×add-cbrt-cube add-exp-log difference-of-squares
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff
2×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
4 → 128
Calls
4 calls:
Slowest
27.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
23.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (* (tan x) (tan x)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
52.0ms
(* (tan x) (tan x))
45.0ms
(- 1 (* (tan x) (tan x)))
43.0ms
(* (tan x) (tan x))

simplify6.5s

Counts
119 → 140
Calls
119 calls:
Slowest
582.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
553.0ms
(/ (- 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1))
381.0ms
(- (pow 1 3) (pow (* (tan x) (tan x)) 3))
332.0ms
(- 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
325.0ms
(+ (* 1 1) (- (* (* (tan x) (tan x)) (* (tan x) (tan x))) (* 1 (* (tan x) (tan x)))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.2b
(* (+ 1 (tan x)) (- 1 (tan x)))
0.2b
(- 1 (tan x))
0.2b
(+ 1 (tan x))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
27×prod-diff
13×pow1
11×distribute-rgt-in distribute-lft-in
9×associate-*r*
8×add-cbrt-cube add-exp-log add-log-exp
7×associate-*l*
5×frac-times
4×expm1-log1p-u flip3-+ flip3-- tan-quot flip-+ insert-posit16 log1p-expm1-u flip-- difference-of-squares
3×sub-neg fma-def fma-neg swap-sqr associate-*l/ associate-*r/
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×pow2 +-commutative sum-log pow-plus diff-log pow-sqr pow-prod-up
Counts
4 → 134
Calls
4 calls:
Slowest
53.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
20.0ms
(* (tan x) (tan x))
5.0ms
(- 1 (tan x))
5.0ms
(+ 1 (tan x))

series176.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(* (+ 1 (tan x)) (- 1 (tan x)))
46.0ms
(* (tan x) (tan x))
26.0ms
(+ 1 (tan x))
22.0ms
(- 1 (tan x))

simplify17.9s

Counts
114 → 146
Calls
114 calls:
Slowest
1.0s
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
953.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
867.0ms
(* (* (* (+ 1 (tan x)) (+ 1 (tan x))) (+ 1 (tan x))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
812.0ms
(* (+ (* 1 1) (- (* (tan x) (tan x)) (* 1 (tan x)))) (+ (* 1 1) (+ (* (tan x) (tan x)) (* 1 (tan x)))))
751.0ms
(- 1 (+ x (* 1/3 (pow x 3))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
143×times-frac
136×add-sqr-sqrt
135×prod-diff
124×*-un-lft-identity
116×add-cube-cbrt
54×associate-/r/
30×div-inv
27×flip3-+ flip-+
25×pow1
15×fma-neg
12×tan-quot
10×add-cbrt-cube add-exp-log
9×swap-sqr associate-*r* associate-*l*
6×add-log-exp difference-of-squares
5×distribute-rgt-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 273
Calls
4 calls:
Slowest
44.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
19.0ms
(* (tan x) (tan x))
18.0ms
(* (tan x) (tan x))
14.0ms
(* (tan x) (tan x))

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))
53.0ms
(* (tan x) (tan x))
48.0ms
(* (tan x) (tan x))
39.0ms
(* (tan x) (tan x))

simplify1.2m

Counts
399 → 285
Calls
399 calls:
Slowest
777.0ms
(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))
743.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ 1 (* (tan x) (tan x)))) (- (* (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))) 1)))
688.0ms
(fma (* (cbrt (/ 1 (+ 1 (* (tan x) (tan x))))) (cbrt (/ 1 (+ 1 (* (tan x) (tan x)))))) (cbrt (/ 1 (+ 1 (* (tan x) (tan x))))) (- (* (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))) 1)))
655.0ms
(fma (- (/ 1 (+ 1 (* (tan x) (tan x))))) (* (tan x) (tan x)) (* (/ 1 (+ 1 (* (tan x) (tan x)))) (* (tan x) (tan x))))
592.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ 1 (* (tan x) (tan x)))) (cbrt (+ 1 (* (tan x) (tan x)))))) (/ (cbrt 1) (cbrt (+ 1 (* (tan x) (tan x))))) (- (* (/ 1 (+ 1 (* (tan x) (tan x)))) (* (tan x) (tan x)))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(exp (+ 1 (tan x)))
0.3b
(* (tan x) (tan x))
0.2b
(log (exp (+ 1 (tan x))))
0.2b
(* (log (exp (+ 1 (tan x)))) (- 1 (tan x)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
33×add-sqr-sqrt
26×add-cube-cbrt
18×prod-diff
15×pow1
12×exp-prod
11×distribute-rgt-in distribute-lft-in associate-*l*
10×log-pow
9×associate-*r*
8×add-cbrt-cube add-exp-log
7×add-log-exp
4×expm1-log1p-u log-prod tan-quot insert-posit16 log1p-expm1-u
3×swap-sqr associate-*r/ distribute-lft-out
2×sub-neg exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×pow2 frac-times sum-log pow-plus flip3-- rem-log-exp associate-*l/ pow-sqr pow-prod-up flip-- distribute-lft-out--
Counts
4 → 121
Calls
4 calls:
Slowest
45.0ms
(* (log (exp (+ 1 (tan x)))) (- 1 (tan x)))
23.0ms
(* (tan x) (tan x))
19.0ms
(log (exp (+ 1 (tan x))))
15.0ms
(exp (+ 1 (tan x)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(* (log (exp (+ 1 (tan x)))) (- 1 (tan x)))
54.0ms
(exp (+ 1 (tan x)))
46.0ms
(* (tan x) (tan x))
31.0ms
(log (exp (+ 1 (tan x))))

simplify11.8s

Counts
93 → 133
Calls
93 calls:
Slowest
958.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
906.0ms
(* (+ (/ (sin x) (cos x)) 1) (- 1 (/ (sin x) (cos x))))
537.0ms
(* (fma (- (sqrt (tan x))) (sqrt (tan x)) (* (sqrt (tan x)) (sqrt (tan x)))) (log (exp (+ 1 (tan x)))))
510.0ms
(* (* (* (log (exp (+ 1 (tan x)))) (log (exp (+ 1 (tan x))))) (log (exp (+ 1 (tan x))))) (* (* (- 1 (tan x)) (- 1 (tan x))) (- 1 (tan x))))
506.0ms
(* (fma (- (sqrt (tan x))) (sqrt (tan x)) (* (sqrt (tan x)) (sqrt (tan x)))) (log (exp (+ 1 (tan x)))))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes378.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.5s1484×body1280valid
1.3s4349×body80valid
1.3s1262×body640valid
520.0ms565×body320valid
298.0ms340×body160valid